BSA Flow Software Installation and User's Guide - CSI

Recipe for block-based statistics
The formulas on the previous pages can be summed up in the following stepby-step
procedure describing what to do when a block of M new data
samples arrives.
A block of samples is assumed to include M samples, each consisting of a
transit time t and two coincident velocity samples U and V. Transit times are
needed only if the user wishes to perform transit time weighting in the
calculation of statistics. If this is NOT desired just set t=1 everywhere in the
following formulas. If samples are not coincident you cannot calculate any
mixed moments, and the user should not be allowed to try, but receive an
error message if attempting to do so.
For statistics on 3D-measurements a third velocity component will be
included. The formulas below can easily be expanded to handle this, and it
will not be described in detail how to do this.
Update 0 th order sums (sample count and sum of transit times):
N ← N + M
∑
( ∑ t)
+ ( t)
N
M
t ← ∑
Update 1 st order sums (sum of weighted velocities):
∑
∑
( ∑ tU)
+ ( tU)
N
M
( ∑ tV)
+ ( tV)
N
M
tU ← ∑
tV ← ∑
Update 1 st order moments (mean-value estimates):
U =
∑ t
∑
U
t
V =
∑ t
∑
Update 2 nd order sums:
∑
∑
V
t
2
2
( ∑ tU
) + ( tU
) N
M
2
2
( ∑ tV
) + ( tV
) N
M
2
tU ← ∑
2
tV ← ∑
Update 2 nd order moments (bias correction term at the end is optional):
7-104 BSA Flow Software: Reference guide